Which irrational number is between 14−−√

Question

and 18−−√
?(1 point)
Responses

15−−√
start root 15 end root

13−−√
start root 13 end root

19−−√
start root 19 end root

10−−√

Answer 1

To find an irrational number between \( \sqrt{14} \) and \( \sqrt{18} \), we can calculate the approximate values of these square roots:

• \( \sqrt{14} \approx 3.74 \)
• \( \sqrt{18} \approx 4.24 \)

Now, we need to check which of the given options falls between these two values:

1. \( \sqrt{15} \):

   • \( \sqrt{15} \approx 3.87 \) (Between 3.74 and 4.24)

2. \( \sqrt{13} \):

   • \( \sqrt{13} \approx 3.61 \) (Less than 3.74)

3. \( \sqrt{19} \):

   • \( \sqrt{19} \approx 4.36 \) (Greater than 4.24)

4. \( \sqrt{10} \):

   • \( \sqrt{10} \approx 3.16 \) (Less than 3.74)

Based on this analysis, the irrational number that lies between \( \sqrt{14} \) and \( \sqrt{18} \) is:

\( \sqrt{15} \).